It has long been known that all electrical resistors are characterized by an inherent noise which is due to the thermal agitation of the free electrons within the resistor material. As used herein, the term "resistor", includes any body of material capable of carrying an electrical current. As such, the term embraces components such as wires and other conductors which are not ordinarily thought of as "resistors". If a signal current in the resistor or conductor is smaller than the random current due to thermal agitation then, as a practical matter, the signal is masked and no amount of amplification can separate them. This noise, known as "thermal noise", "Johnson noise" or "white noise", has heretofore generally been accepted as one of the limiting factors in the design of low-level signal processing circuits.
From the research of Johnson and Nyquist in the late 1928's, it is known that the thermal noise voltage across the open ends of a resistor is determined by the formula: EQU e.sub.n.sup.2 =4kTRB [1]
Where e.sub.n.sup.2 is the average of the square of the noise voltage; k is Boltzmann's constant (1.138.times.10.sup.-23 joules per K); T is the absolute temperature of the conductor in .degree.K.; R is the resistor or conductor in ohms; and B is the bandwidth in Hertz over which the noise is measured.
In order to reduce the thermal noise of a given resistance R, it is seen from Equation [1] that either the temperature (T) or the bandwidth (B) must be reduced. To reduce B, of course, is generally not possible, since the operational bandwidth of a circuit is ordinarily predetermined and not susceptible to casual manipulation. In general, therefore, it has been the practice to minimize the thermal noise of a circuit by cooling the resistor or the entire circuit, in some cases to cryogenic temperatures. However, since the noise voltage is proportional to the square root of the absolute temperature, it is readily appreciated that it is both costly and cumbersome to provide the degree of cooling required to achieve a significant reduction in thermal noise.
It is therefore an object of the present invention to provide a non-cryogenically cooled low-noise temperature resistance.
In 1939, it was suggested by W. S. Percival that a simulated resistor having an effective noise temperature lower than ambient temperature could be realized by feedback means. (See: W. S. Percival, "An Electrically `Cold` Resistance", The Wireless Engineer, Vol. 16, May 1939, pp. 237-240). By utilizing a single transformer between the plate and grid of a vacuum tube amplifier, Percival simulated a resistance having an effective temperature of 70.degree. K. The same technique was later expanded upon by Strutt and Van der Ziel in an article entitled, "Suppression of Spontaneous Fluctuations in Amplifiers and Receiver for Electrical Communication and For Measuring Devices," Physica, Vol. 9, No. 6, June 1942, pp. 513-527. Professor Van der Ziel also briefly summarized the techniques in his treatise "Noise," Prentice-Hall, New York, N.Y., 1954, pp. 262 et seq. (See also: U.S. Pat. No. 2,352,956 which issued to M. J. O. Strutt, et al. on July 4, 1944. )
The circuits of the prior art appear to have received little attention in the several decades since their introduction. This may be due to the many shortcomings inherent in the use of vacuum tubes such as their high operating temperatures and the other sources of noise inherent therein. In any event, advances in solid state technology have produced a number of sophisticated, highly efficient, low-cost active devices which allow the synthesis of economical low-noise temperature resistance simulating circuits.
It is therefore another object of the present invention to provide an active circuit which simulates a low-noise resistor.
A recent attempt at reducing circuit noise by feedback means is illustrated in U.S. Pat. No. 3,839,686 which was issued to W. Vogel on Oct. 1, 1974. According to the teachings of that invention, the induced voltage on a transmission line such as a coaxial cable can be decreased by a feedback control circuit which includes an amplifier. Although the circuit of the Vogel patent does not simulate a resistance, either low-noise or otherwise, it does represent an example of noise reduction employing feedback techniques.
More recent techniques for simulating low-noise temperature resistors have been suggested in copending U.S. Patent Applications: Ser. No. 838,511, filed Oct. 3, 1977, now U.S. Pat. No. 4,156,859; and Ser. No. 881,296, filed Feb. 27, 1978, now U.S. Pat. No. 4,176,331. Another suggested circuit which utilizes a feedback amplifier as the active circuit element is described in a paper in Radio and Electronic Engineer, Vol. 42, No. 4, April 1972, pp. 163-171. In each of the several sources mentioned above, the circuits are unlike those of the present invention.